For this group assignment, each group should work on the two following questions. Please note that the final answer is not enough, you should show the work for full credit.

$1.$ Customers arrive at Rent$-$a$-$Wreck store and hope to score an inexpensive and unsightly vehicle to use for a short period of time. About thirty customers show up at any hour of the day and it takes the customer service representative about $1\mathrm{.}5$ minutes to photocopy their driver's license and insurance card and take an impression of a credit card. Assume that the service and arrival rates are governed by the Poisson distribution.

$1$a$.$ Calculate the utilization rate.

$1$b$.$ What is the average number of people waiting in the line?

$1$c$.$ What is the average waiting time in the line?

$1$d$.$ What is the average number of people in the store?

$1$e$.$ What is the average time customers spend in the store?

$1$f$.$ How much time the customer service representative is idle in an hour?

$2.$ An entrepreneur identifies a product called X that she knows will sell well if she can only figure out a way to bring it to her area. The entrepreneur has identified three ways to bring X to the masses; she can import it$,$ she can try to produce it on her own, and she can have a local reputable producer make it for her $($outsource$).$ The fixed and variable costs for each of these alternatives are shown below.

Import Produce Outsource

Fixed Cost $$25,000$ $$500,000$ $$0$

Variable Cost $$30$ $$10$ $$37$

$2$a$.$ Develop a graph showing the ideal alternative across a range of demands that reflects all decision points.

$2$b$.$ What is the best decision for each quantity of the products?

$3.$ A company with fixed costs of $$382,700$ and a target price of $$560$ for its sole product, a heat shield for masonry fireplaces. What level of output represents their break$-$even point if their variable cost for producing is $$115$ per unit?